Fabregas came off the bench in the second half to mark his debut for the Catalans in an ill-tempered 3-2 victory over Madrid.
The former Arsenal skipper played a part in the build-up to Lionel Messi's winner two minutes from time and later was on the receiving end of a crude challenge from Marcelo which sparked angry confrontatios between both sets of players and their benches.
Marcelo was given a straight red for his tackle on Fabregas while Mesut Ozil and David Villa, who were both taken off in the second half, were also shown red cards for their role in the mass brawl.
"This is very competitive football, we are talking about the two best clubs in the world and every team wants to win," Fabregas told reporters after the game.
"This is normal in football that a situation like this can happen.
"It's always good to start well, with positive situations like this. I am very happy. They had just scored when I went into the pitch and I was just thinking in helping my team."
The scores were level at 2-2 from the first leg last week, before Lionel Messi set up Andres Iniesta for the early opener on Wednesday night. The lead lasted only five minutes as Cristiano Ronaldo equalised but Messi stuck soon afterwards to restore Barca's lead.
Karim Benzema brought the visitors level eight minutes from time but Barca had Messi to thank again as he volleyed home the winner with just two minutes to spare in the game.
Barcelona won the match 3-2 to lift the Supercopa 5-4 on aggregate.